This book provides a comprehensive presentation of the conceptual basis of wavelet analysis, including the construction and analysis of wavelet bases. It motivates the central ideas of wavelet theory by offering a detailed exposition of the Haar series, then shows how a more abstract approach allows readers to generalize and improve upon the Haar series. It then presents a number of variations and extensions of Haar construction.
Inhalt
Preface
Part I: Preliminaries
Functions and Convergence
Fourier Series
The Fourier Transform
Signals and Systems
Part II: The Haar System
The Haar System
The Discrete Haar Transform
Part III: Orthonormal Wavelet Bases
Mulitresolution Analysis
The Discrete Wavelet Transform
Smooth, Compactly Supported Wavelets
Part IV: Other Wavelet Constructions
Biorthogonal Wavelets
Wavelet Packets
Part V: Applications
Image Compression
Integral Operators
Appendix A: Review of Advanced Calculus and Linear Algebra
Appendix B: Excursions in Wavelet Theory
Appendix C: References Cited in the Text
Index